Defeat to Arsenal on Saturday means that the Reds now sit 10 points behind the fourth-placed Gunners with just 12 games remaining.
However, the Slovakian believes that winning a second domestic trophy - after success in the League Cup in February - would overcome any disappointment amongst fans and players after missing out on the top four.
"The aim was always to reach the Champions League places and win a cup," he told reporters.
"There is no point in letting all our efforts so far come to nothing. It would be really successful if we could win two cups."
Liverpool are 11/2 with Sportingbet to end the season in the Premier League top four.
Skrtel has been a key part of a mean Reds defence this season, consigning club legend Jamie Carragher to the bench for much of the campaign.
And the defender cited Welsh forward Craig Bellamy as an inspiration on the training ground, saying that the former Manchester City man has pushed him to improve.
He told the club's official matchday programme: "You see people like Bellars [Bellamy]; ones who give everything every day. He has been very successful for a long time but he still wants to be the best.
"You have to have that attitude. I am 27 now and I think I can still improve.
"Experience has a lot to do with it. As you get older you learn how to deal with success and failure and I feel a lot more confident in my ability to make the right decisions."